Multipliers of double Fourier-Haar series

The multipliers of double Fourier-Haar series for functions from anisotropic Lorentz spaces are investigated. Necessary and sufficient conditions are obtained for the sequence lambda = {lambda(j1j2)(k1k2)} to belong to the class m(L-(p) over bar,L-(r) over bar -> L-(q) over bar,L- (s) over bar). In particular, the case is described when (s) over bar<<(r)over bar>, which is a new result in the one-dimensional case as well.